Regular
Algebras

Regular algebras axiomatise the equational theory of regular expressions as induced by
regular language identity. We use Isabelle/HOL for a detailed systematic study of regular
algebras given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between
these classes, formalise a soundness proof for the smallest class (Salomaa's) and obtain
completeness of the largest one (Boffa's) relative to a deep result by Krob. In addition
we provide a large collection of regular identities in the general setting of Boffa's axiom.
Our regular algebra hierarchy is orthogonal to the Kleene algebra hierarchy in the Archive
of Formal Proofs; we have not aimed at an integration for pragmatic reasons.